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Full text of "Treatise On Analysis Vol-Ii"

viii        CONTENTS

group. 6. Examples and particular cases of convolution of measures.
7. Algebraic properties of convolution. 8. Convolution of a measure and a func-
tion. 9. Examples of convolutions of measures and functions. 10. Convolution
of two functions. 11. Regularization.

Chapter XV

NORMED ALGEBRAS AND SPECTRAL THEORY     ........304

1. Normed algebras. 2. Spectrum of an element of a normed algebra. 3. Charac-
ters and spectrum of a commutative Banach algebra. The Gelfand transformation.
4. Banach algebras with involution. Star algebras. 5. Representations of algebras
with involution. 6. Positive linear forms, positive Hilbert forms, and representa-
tions. 7. Traces, bitraces, and Hilbert algebras. 8. Complete Hilbert algebras.
9. The Plancherel-Godement theorem. 10, Representations of algebras of con-
tinuous functions. 11. The spectral theory of Hilbert. 12. Unbounded normal
operators. 13. Extensions of hermitian operators.

References...................   . m......444

Index.............................447                                    set of elements xy with x e A and y e B,